Finite Group Databasebeta

← C2×#19135842 #25124280

Subgroups — C2×#19135842 #25124280

Order 11008.

1542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063325C211yesmaximal, characteristic
2C22×#13063250C212yesmaximal
3C22×#13063250C212yesmaximal
4C2×#14582797C211yesmaximal, characteristic
5#19135842C218yesmaximal, direct product factor
6C2×C43×#336C211yesmaximal, characteristic
7C23×Dic86C2212yes—
8C2×#13063325—28no—
9C2×#13063325—22no—
10C2×#13063325C2214yes—
11C22×C4⋊Dic43—21no—
12C22×C4⋊Dic43—21no—
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4—21no—
16C2×#13063250—28no—
17C2×#13063250—28no—
18C2×#13063250C2218yes—
19C2×#13063250C2218yes—
20#14582797—22no—
21#14582797C2214yes—
22C2×C43⋊#95—21no—
23C23×C8×C43C2212yes—
24C22×C42×C43C2211yescharacteristic
25C43×#336C2214yes—
26C22×Dic86—24no—
27C22×Dic86—24no—
28C22×Dic86—24no—
29C22×Dic86—24no—
30C22×Dic86—22no—
31C22×Dic86—24no—
32C22×Dic86D418yes—
33C22×Dic86C2314yes—
34C23×Dic43—21no—
35C23×Dic43—22no—
36C23×Dic43—21no—
37#13063325—216no—
38#13063325—216no—
39C2×C4⋊Dic43—28no—
40C2×C4⋊Dic43—28no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—24no—
43C2×C4⋊Dic43—24no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—24no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43D414yes—
48C2×C4⋊Dic43C2312yes—
49C2×C4⋊Dic43C2312yes—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—44no—
52#13063250—216no—
53#13063250—216no—
54C43⋊#95—24no—
55C23×C4×C43D411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C22×C8×C43—24no—
59C22×C8×C43—24no—
60C22×C8×C43—24no—
61C22×C8×C43C2314yes—
62C2×C42×C43—24no—
63C2×C42×C43D412yes—
64C2×C42×C43C2312yes—
65C24×C43C2×D411yescharacteristic
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43SD1614yes—
71C22×C4×C43Q1614yes—
72C22×C4×C43C2×D414yes—
73C22×C4×C43C2×D412yes—
74C22×C4×C43C2×D412yes—
75C22×C4×C43C2×D412yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4112yes—
78C22×C4×C43#4114yes—
79C22×C4×C43C2411yescharacteristic
80C22×Dic43—28no—
81C22×Dic43—24no—
82C22×Dic43—22no—
83C22×Dic43—24no—
84C22×Dic43—22no—
85C22×Dic43—42no—
86C22×Dic43—44no—
87C22×Dic43—44no—
88C22×Dic43—42no—
89C22×Dic43—42no—
90C22×Dic43—42no—
91C22×Dic43—42no—
92C2×Dic86—216no—
93C2×Dic86—216no—
94C2×Dic86—24no—
95C2×Dic86—24no—
96C2×Dic86—24no—
97C2×Dic86—24no—
98C2×Dic86—28no—
99C2×Dic86—24no—
100C2×Dic86—48no—
101C2×Dic86—44no—
102C2×Dic86—48no—
103C2×Dic86—44no—
104C2×Dic86C2×D418yes—
105C2×C8×C43—24no—
106C2×C8×C43—24no—
107C2×C8×C43—24no—
108C2×C8×C43—48no—
109C42×C43—24no—
110C42×C43—24no—
111C4⋊Dic43—216no—
112C4⋊Dic43—216no—
113C4⋊Dic43—24no—
114C4⋊Dic43—22no—
115C4⋊Dic43—24no—
116C4⋊Dic43—42no—
117C4⋊Dic43C2×D414yes—
118Dic43⋊C4—48no—
119C23×C43#12012yes—
120C23×C43#12112yes—
121C23×C43#12412yes—
122C23×C43C2×SD1612yes—
123C23×C43C2×Q1612yes—
124C23×C43#13712yes—
125C23×C43#13712yes—
126C23×C43C22×D411yescharacteristic
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—28no—
132C2×C4×C43—28no—
133C2×C4×C43#12012yes—
134C2×C4×C43#12118yes—
135C2×C4×C43#12112yes—
136C2×C4×C43#12318yes—
137C2×C4×C43#12412yes—
138C2×C4×C43C2×SD1614yes—
139C2×C4×C43C2×Q1614yes—
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C22×D412yes—
142C2×C4×C43C2×#4112yes—
143C2×C4×C43C2×#4111yescharacteristic
144C2×Dic43—28no—
145C2×Dic43—24no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—416no—
151C2×Dic43—48no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—84no—
156Dic86—28no—
157Dic86—28no—
158Dic86—44no—
159Dic86—44no—
160Dic86—416no—
161C8×C43—44no—
162C2×#2043—431nomaximal, Sylow
163C22×C43#39414yes—
164C22×C43#44814yes—
165C22×C43#45114yes—
166C22×C43#46114yes—
167C22×C43#46214yes—
168C22×C43#48714yes—
169C22×C43#49114yes—
170C22×C43C2×#12011yescharacteristic
171C22×C43C2×#12111yescharacteristic
172C22×C43C2×#12411yescharacteristic
173C22×C43C22×SD1611yescharacteristic
174C22×C43C22×Q1611yescharacteristic
175C22×C43C2×#13711yescharacteristic
176C22×C43C2×#13711yescharacteristic
177C4×C43—24no—
178C4×C43—24no—
179C4×C43#39414yes—
180C4×C43C2×#12112yes—
181C4×C43C2×#12312yes—
182Dic43—48no—
183Dic43—44no—
184Dic43—82no—
185C22×C4⋊Q8—431no—
186C22×#103—432no—
187C22×#103—432no—
188C2×#389—431no—
189#2043—438no—
190C2×#336D4311yescharacteristic
191C2×C43#204318yescomplemented
192C2×C43C2×#39411yescharacteristic
193C2×C43C2×#44811yescharacteristic
194C2×C43C2×#45111yescharacteristic
195C2×C43C2×#46111yescharacteristic
196C2×C43C2×#46211yescharacteristic
197C2×C43C2×#48711yescharacteristic
198C2×C43C2×#49111yescharacteristic
199C23×Q8—432no—
200C23×C8C2×D4312yes—
201C2×C4⋊Q8—434no—
202C2×C4⋊Q8—868no—
203C2×C4⋊Q8—862no—
204C22×C4⋊C4—431no—
205C22×C4⋊C4—431no—
206C22×C4⋊C4—861no—
207C22×C4⋊C4—861no—
208C22×C4⋊C4—861no—
209C22×C42C2×D4311yescharacteristic
210C2×#103—438no—
211C2×#103—438no—
212C2×#103—868no—
213C2×#103—868no—
214#389—434no—
215#389—862no—
216C2×#95—861no—
217#336C2×D4314yes—
218C43C2×#204311yescharacteristic, complemented, Sylow
219C22×Q8—438no—
220C22×Q8—434no—
221C22×Q8—862no—
222C22×Q8—864no—
223C22×Q8—864no—
224C22×Q8—864no—
225C22×Q8—864no—
226C22×Q8—864no—
227C23×C4—861no—
228C23×C4—862no—
229C23×C4—861no—
230C23×C4D17211yescharacteristic
231C23×C4D17211yescharacteristic
232C23×C4C22×D4311yescharacteristic
233C22×C8—24no—
234C22×C8—24no—
235C22×C8—24no—
236C22×C8C22×D4314yes—
237C4⋊Q8—8616no—
238C4⋊Q8—8616no—
239C2×C4⋊C4—434no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—432no—
242C2×C4⋊C4—868no—
243C2×C4⋊C4—868no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—864no—
246C2×C4⋊C4—864no—
247C2×C4⋊C4—862no—
248C2×C4⋊C4—864no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—864no—
251C2×C4⋊C4—1724no—
252C2×C42—24no—
253C2×C42D17212yes—
254C2×C42C22×D4312yes—
255#103—8616no—
256#103—8616no—
257#95—864no—
258C24C2×D17211yescharacteristic
259C2×Q8—438no—
260C2×Q8—868no—
261C2×Q8—864no—
262C2×Q8—8616no—
263C2×Q8—8616no—
264C2×Q8—864no—
265C2×Q8—864no—
266C2×Q8—864no—
267C2×Q8—864no—
268C2×Q8—1728no—
269C2×Q8—1724no—
270C2×Q8—1728no—
271C2×Q8—1724no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—868no—
277C22×C4—864no—
278C22×C4—862no—
279C22×C4—864no—
280C22×C4—862no—
281C22×C4—1722no—
282C22×C4—1722no—
283C22×C4—1722no—
284C22×C4—1724no—
285C22×C4—1724no—
286C22×C4—1722no—
287C22×C4—1722no—
288C22×C4#1062187314yes—
289C22×C4Dic17214yes—
290C22×C4C2×D17212yes—
291C22×C4C2×D17212yes—
292C22×C4C2×D17211yescharacteristic
293C22×C4#1062189814yes—
294C22×C4D4×D4314yes—
295C22×C4D4×D4312yes—
296C22×C4#1062190212yes—
297C22×C4C23×D4311yescharacteristic
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—24no—
301C2×C8—48no—
302C4⋊C4—434no—
303C4⋊C4—8616no—
304C4⋊C4—8616no—
305C4⋊C4—864no—
306C4⋊C4—862no—
307C4⋊C4—864no—
308C4⋊C4—1722no—
309C4⋊C4—1728no—
310C42—24no—
311C42—24no—
312C23#1306329512yes—
313C23#1306330012yes—
314C23#1306331312yes—
315C23C2×#1062187312yes—
316C23C2×Dic17212yes—
317C23#1306335812yes—
318C23#1306335812yes—
319C23C22×D17211yescharacteristic
320Q8—868no—
321Q8—868no—
322Q8—17216no—
323Q8—1724no—
324Q8—1724no—
325C2×C4—28no—
326C2×C4—28no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—868no—
332C2×C4—864no—
333C2×C4—3444no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—17216no—
338C2×C4—1728no—
339C2×C4—1724no—
340C2×C4—1724no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4#1306329512yes—
344C2×C4#1306329818yes—
345C2×C4#1306330012yes—
346C2×C4#1306331018yes—
347C2×C4#1306331312yes—
348C2×C4C2×#1062187314yes—
349C2×C4C2×Dic17214yes—
350C2×C4C2×D4×D4311yescharacteristic
351C2×C4C2×D4×D4312yes—
352C2×C4C2×#1062189812yes—
353C2×C4C2×#1062190211yescharacteristic
354C8—44no—
355C22#1458281714yes—
356C22#1458304014yes—
357C22#1458305714yes—
358C22#1458310514yes—
359C22#1458311014yes—
360C22#1458325014yes—
361C22#1458326814yes—
362C22C2×#1306329511yescharacteristic
363C22C2×#1306330011yescharacteristic
364C22C2×#1306331311yescharacteristic
365C22C22×#1062187311yescharacteristic
366C22C22×Dic17211yescharacteristic
367C22C2×#1306335811yescharacteristic
368C22C2×#1306335811yescharacteristic
369C4—24no—
370C4—24no—
371C4—3442no—
372C4—1728no—
373C4—1724no—
374C4#1458281714yes—
375C4C2×#1306329812yes—
376C4C2×#1306331012yes—
377C2#1913584218yesdirect product factor
378C2C2×#1458281711yescharacteristic
379C2C2×#1458304011yescharacteristic
380C2C2×#1458305711yescharacteristic
381C2C2×#1458310511yescharacteristic
382C2C2×#1458311011yescharacteristic
383C2C2×#1458325011yescharacteristic
384C2C2×#1458326811yescharacteristic
subgroupG/H
centerC24C2×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#336C2
socle, prime radicalC24×C43C2×D4
hypercenterC2×#336D43
hypocenterC43C2×#2043
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #19135842C2direct (N × H)
191. C2×C43#2043semidirect
218. C43C2×#2043semidirect
377. C2#19135842direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130633252
C22×#130632502
C2×#145827972
#191358422
C2×C43×#3362
C2×#204343